the 1 isometry classes of irreducible [15,11,5]_16 codes are:

code no       1:
================
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
4 3 2 1 0 1 0 0 0 0 0 0 0 0 0
3 8 5 1 0 0 1 0 0 0 0 0 0 0 0
11 15 6 1 0 0 0 1 0 0 0 0 0 0 0
15 9 7 1 0 0 0 0 1 0 0 0 0 0 0
12 6 8 1 0 0 0 0 0 1 0 0 0 0 0
10 4 9 1 0 0 0 0 0 0 1 0 0 0 0
7 13 10 1 0 0 0 0 0 0 0 1 0 0 0
8 14 11 1 0 0 0 0 0 0 0 0 1 0 0
5 11 12 1 0 0 0 0 0 0 0 0 0 1 0
9 2 13 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 120
and is strongly generated by the following 4 elements:
(
3 0 0 0 
1 13 11 15 
6 11 7 8 
7 3 5 9 
, 0
, 
15 0 0 0 
4 6 9 11 
7 11 1 5 
12 5 8 14 
, 3
, 
2 3 6 13 
1 4 5 9 
6 8 11 3 
13 9 1 2 
, 1
, 
6 8 15 2 
0 1 0 0 
2 10 9 6 
0 0 0 1 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(2, 14)(3, 11)(4, 13)(5, 15)(6, 10)(7, 8)(9, 12), 
(2, 5, 8, 9)(3, 6, 11, 10)(4, 13)(7, 12, 14, 15), 
(1, 6, 3, 11)(2, 8, 4, 12)(5, 7, 14, 13), 
(1, 13)(3, 7)(5, 6)(9, 10)(11, 14)
orbits: { 1, 11, 13, 3, 6, 14, 4, 10, 7, 5, 2, 12, 8, 9, 15 }